Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The budgeted maximum coverage problem
Information Processing Letters
Information and Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An Algebraic Model for Combinatorial Problems
SIAM Journal on Computing
Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Generalized Maximum Coverage Problem
Information Processing Letters
Information Processing Letters
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
| Hi-index | 0.00 |
An instance of the maximum coverage problem is given by a set of weighted ground elements and a cost weighted family of subsets of the ground element set. The goal is to select a subfamily of total cost of at most that of a given budget maximizing the weight of the covered elements.We formulate the problem on graphs: In this situation the set of ground elements is specified by the nodes of a graph, while the family of covering sets is restricted to connected subgraphs. We show that on general graphs the problem is polynomial time solvable if restricted to sets of size at most 2, but becomes NP-hard if sets of size 3 are permitted. On trees, we prove polynomial time solvability if each node appears in a fixed number of sets. In contrast, if vertices are allowed to appear an unbounded number of times, the problem is NP-hard even on stars. We finally give a polynomial time algorithm for the special case where a star is covered by paths.